Blow-up rates of radially symmetric large solutions

Abstract: This paper adapts a technical device going back to [J. López-Gómez, Optimal uniqueness theorems and exact blow-up rates of large solutions, J. Differential Equations 224 (2006) 385–439] to ascertain the blow-up rate of the (unique) radially symmetric large solution given through the main theorem of [J. López-Gómez, Uniqueness of radially symmetric large solutions, Discrete Contin. Dyn. Syst., Supplement dedicated to the 6th AIMS Conference, Poitiers, France, 2007, pp. 677–686]. The requested underlying estimates are based upon the main theorem of [S. Cano-Casanova, J. López-Gómez, Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line, J. Differential Equations 244 (2008) 3180–3203]. Precisely, we show that if Ω is a ball, or an annulus, is positive and non-decreasing, satisfies , , , for every , and as , for some and , then, for each , possesses a unique positive large solution in Ω, L, which must be radially symmetric, by uniqueness, and we can estimate the exact blow-up rate of at ∂Ω in terms of p, H and f (see Theorem 1.1). [Copyright &y& Elsevier]